minimum value.

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The minimum value of
x² + 2xy + 3y² â€“ 6x â€“ 2y, where x, y are Real , is equal
to
(a) â€“9
(b) â€“11
(c) â€“12
(d) â€“10

#Mathematics #Algebra

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8 Answers

262

Aditya Bhutra ·2011-09-03 23:25:32

ans -9 ??

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1

fahadnasir nasir ·2011-09-04 00:09:00

The answar is (b)

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rishabh ·2011-09-04 01:14:42

can some1 pls factorise this expression?

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11

Devil ·2011-09-04 03:34:57

The given expression is (x+y)²-6(x+y)+2y²+4yâ‰¥-11

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johncenaiit ·2011-09-04 06:13:58

pls explain why the expression is â‰¥ -11 ?

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21

Shubhodip ·2011-09-04 08:06:04

i dont think there is an immediate conclusion from writing it as (x+y)^2-6(x+y)+2y^2+4y

other than (x+y-3)^2 + 2(y+1)^2 -11

:D

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11

Devil ·2011-09-04 21:28:16

A quadratic whose leading coefficient is positive is minimised at x=-b2a.

(x+y)²-6(x+y)â‰¥-9

same logic for 2y²+4yâ‰¥-2

sigh :-(

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rishabh ·2011-09-05 10:04:54

can some1 pls post more sums of this type in this thread.
i have to improve my "factoisational" skills.

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